The class of width-two orders has a model companion. The model companion is complete, decidable, non-finitely axiomatizable, and has continuum many countable models. Generalizations of some results in (Pouzet, M., 1978, J. Combin. Theory Ser. B 25) are presented in the width-n case, for n > 2. Mathematics Subject Classifications (1991): 06A06, 03C52.